With the rapid development of deep buried traffic tunnels, underground space utilization, and global energy resource extraction, the scale of deep underground engineering continues to expand. These trends place increasing demands on understanding the mechanical behavior of rock under high in-situ stress conditions. However, traditional discrete element models, constrained by constant stiffness assumptions, often over-linearize the compaction stage and have difficulty capturing tangent modulus evolution across confining pressures. To address this limitation, this study integrated triaxial test data for multiple lithologies, including granite, slate, and sandstone, and identified a robust exponential relationship between the tangent modulus in the compaction stage and mean stress. Building on this observation, a variable stiffness parallel bond model was developed. The model established a real-time mapping between contact stiffness and contact stress and incorporated a three-state judgment mechanism that enables adaptive stiffness updating. Furthermore, based on the theoretical correlation of stress states, a multi-confining-pressure calibration strategy was introduced. By adopting a method of parameter selection from multiple benchmark conditions combined with interpolation verification, this approach effectively resolves the non-uniqueness issue inherent in micro-macro parameter mapping. Validation using triaxial compression tests on carbonaceous slate over a wide confining pressure range demonstrated that the proposed model can accurately reproduce the morphology of full stress-strain curves. The relative error in peak strength remains within a small margin. The model also systematically captured key pressure-sensitive responses, including the shortening of the compaction stage, peak strength enhancement, and the brittle-ductile transition. Overall, the proposed model provides a high-fidelity numerical tool for predicting rock behavior in deep environments.
Wang et al. (Tue,) studied this question.